Inverse theorems for some linear positive operators using Beta and Baskakov basis functions

2021 ◽  
Author(s):  
Lakshmi Narayan Mishra ◽  
A. Srivastava ◽  
T. Khan ◽  
S. A. Khan ◽  
Vishnu Narayan Mishra
Keyword(s):  
Positive Operators ◽  
Basis Functions ◽  
Linear Positive Operators ◽  
Inverse Theorems

scholarly journals On difference of operators with different basis functions

Filomat ◽  
2019 ◽  
Vol 33 (10) ◽  
pp. 3023-3034 ◽  
Author(s):  
Vijay Gupta ◽  
Ana Acu
Keyword(s):  
Quantitative Estimate ◽  
Classical Result ◽  
Positive Operators ◽  
Basis Functions ◽  
Linear Positive Operators ◽  
Numerical Examples ◽  
Difference Of Operators ◽  
The Difference

In the recent years several researchers have studied problems concerning the difference of two linear positive operators, but all the available literature on this topic is for operators having same basis functions. In the present paper, we deal with the general quantitative estimate for the difference of operators having different basis functions. In the end we provide some examples. The estimates for the differences of two operators can be obtained also using classical result of Shisha and Mond. Using numerical examples we will show that for particular cases our result improves the classical one.

On the approximation of convex functions using linear positive operators

2017 ◽  
Vol 26 (2) ◽  
pp. 137-143
Author(s):  
DAN BARBOSU
Keyword(s):  
Convex Functions ◽  
Remainder Term ◽  
Mean Value ◽  
Positive Operators ◽  
Linear Functionals ◽  
Linear Positive Operators ◽  
Famous Theorem ◽  
Approximation Formulas ◽  
Phd Thesis ◽  
Higher Order Convexity

The goal of the paper is to present some results concerning the approximation of convex functions by linear positive operators. First, one recalls some results concerning the univariate real valued convex functions. Next, one presents the notion of higher order convexity introduced by Popoviciu [Popoviciu, T., Sur quelques propri´et´ees des fonctions d’une ou deux variable r´eelles, PhD Thesis, La Faculte des Sciences de Paris, 1933 (June)] . The Popoviciu’s famous theorem for the representation of linear functionals associated to convex functions of m−th order (with the proof of author) is also presented. Finally, applications of the convexity to study the monotonicity of sequences of some linear positive operators and also mean value theorems for the remainder term of some approximation formulas based on linear positive operators are presented.

Iterative combinations for Srivastava–Gupta operators

2020 ◽  
pp. 2150108
Author(s):  
Prerna Maheshwari Sharma
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Simultaneous Approximation ◽  
Higher Order ◽  
Positive Operators ◽  
Integral Type ◽  
Linear Positive Operators ◽  
General Family ◽  
Special Cases

In the year 2003, Srivastava–Gupta proposed a general family of linear positive operators, having some well-known operators as special cases. They investigated and established the rate of convergence of these operators for bounded variations. In the last decade for modified form of Srivastava–Gupta operators, several other generalizations also have been discussed. In this paper, we discuss the generalized modified Srivastava–Gupta operators considered in [H. M. Srivastava and V. Gupta, A certain family of summation-integral type operators, Math. Comput. Modelling 37(12–13) (2003) 1307–1315], by using iterative combinations in ordinary and simultaneous approximation. We may have better approximation in higher order of modulus of continuity for these operators.

scholarly journals TheΘ-transformation of certain positive linear operators

1996 ◽  
Vol 19 (4) ◽  
pp. 667-678 ◽  
Author(s):  
Aleandru Lupaş ◽  
Detlef H. Mache
Keyword(s):  
Construction Method ◽  
Positive Operators ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Order Of Approximation ◽  
Linear Positive Operators

The intention of this paper is to describe a construction method for a new sequence of linear positive operators, which enables us to get a pointwise order of approximation regarding the polynomial summator operators which have “best” properties of approximation.

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